Rhaegar and Lyanna is the most popular theory. And it makes way more sense for Eddard to hide the truth from Robert under that theory. It doesn't appear that Robert was anywhere near Lyanna around the start of the rebellion when Jon was conceived.

If robert was the father why would Ned or Robert want it hidden? Jon would have been the son of his one true love. I think he would have loved him more then the children he thought was his by Cersei.
I would really like to hear more of what you all think. Im pretty new to reddit and find this subreddit my instant favorite.